Question

: In the general form of the G.P, a, ar, \[a{{r}^{2}}\], \[a{{r}^{3}}\], …… What is r?
a)Term
b)Common difference
c)Common ratio
d)Constant

Answer 1

Hint: The given problem is related to geometric progression. Try to recall the various terminologies used in geometric progression and their meanings.

Complete step-by-step answer:
The geometric progression is the sequence in each term derived by multiplying or dividing the previous term by the fixed number. The fixed number which multiplies or divides with the fixed number to the preceding term is called the Common ratio. It is denoted by r.

Let's take the start of the sequence by the term 'a' then the sequence follows as a, ar, \[a{{r}^{2}}\],............

Let the given series be a, b, c,... Here, the common ratio is defined as r=a/b=c/b.

And the general term is defined as \[{{t}_{n}}=a{{r}^{n}}\]. Hence, r is the common ratio. So, the correct option is option (c).


Note: Mainly the students are confused between common ratio and common difference. The common difference is the terminology used at the arithmetic progression(A. P).
The arithmetic progression is defined as the sequence to which the difference between two consecutive terms is the same throughout the sequence. The difference between the consecutive terms is defined as a common difference. It is generally denoted by ‘d’.
Let consider the start of the sequence as 'a' then the sequence followed by a, a+d, a+2d,.......
If the sequence is given by a, b, c, ……… then the common difference is defined as d = a-b = c-b.
And the general term is \[{{t}_{n}}=a+(n-1)d\].